Good pieces of work, Papageno and Brabo. I had a very tense work of the ending just after the game Giri-Nakamura, using every source I could (the forum and some old threads, the article of Luis Rodi Maletich, the scan of an article by Van der Weide/Bosch from Nic Magazine 98 I got with the help of a chesspub member (Parisestmagique) and a response of that article in another NiC Magazine.) I used my engine with many "handplay" and trial-error.
I wanted to publish some analysis but I didn't because I wanted to keep it a bit secret for a moment. But you are close to my conclusions now. After a lot of work, my conclusion was one day "White is winning", one day "there is a defense for Black" until I have found a new demolition. Today, my conclusion is: the ending is really complicate, but the way most White player plays it is draw. I am not sure if Black can draw against best play, I have found very promising queen's ending for White but I don't know if it's winning or not, too complicated...
I have constructed a big file in chessposition trainer on that ending, but I am not very good to do pgn like you did. The pgn here is just to respond to Papageno.
31..Kc6 is a better try than 31..Kb5 (like you, I have found that 31..Kb5 is losing to h5!!)
After 31..Kc6!, the game is still very hard for Black.
Here are some of the rules I had wrote for myself, and some of them were cited by Brabo and others:
1)Black has to come as quickly as possible to c6, with the King, and it must be via f8.
2) a quick d5 is possible for Black when White push b5 alone.
3) a6 should be play only after White play a4 AND f4. (of course there are exceptions)
4) e6 should be played as fast as possible to not allow a way for White to come on d5 with the King
5) Black should probably play h6 against h4, but have to be really careful to not play ..g5 automatically because of the break with h5+f4 from White. It's not so clear when it's the last moment for Black to play h6, probably when White is able to push the g-pawn to g5. It may be an useful "waiting move" to play h6 automatically after h4.
6) The White idea of f4-f5-f6 followed by e5 with the idea to enter with the King, allowing Black to queen first as Rittner-Arnlind is always dangerous. When White play that idea after h5 gxg5 gxh5, it should be easy draw for Black. When EACH kingside pawns are blocked, that same idea doesn't work for White when in the queenside, White has a4+b4 against a6. because there is no Zugwzwang possible.
7) Another dangerous plan: h4 played followed by g4 and h5 to FORCE Black to take on h5 or White will break with f4. But that idea works mostly with the a pawn still on a2, to let the White king come to a5.
8) When White has played h4/g4/f4/e4 b4/a4, Black can't play without a6, because Rittner-Arnlind wins for White.
9) When White plays a quick g4 without h4, g5 is generally good for Black
10) the most promising idea for White is to come as fast as possible in c4 with the king, followed by h4!, then g4, then b4 and f4, and to keep the pawn in a2. That idea of keeping the pawn in a2 seems to be totally new ( I have checked every published games of this ending, corr and OTB) and I have found it while I was working on it, and Brabo seems to have found that too.
So, the most dangerous line I have found is what Brabo and Papageno are discussing, the line of the pgn I put. And after 31..Kc6, White should play 32.g5!! (the most promising to me) or 32.Ka4! (still very promising, and Black has to play 32..f6)
My work here continue to queen's endings with a pawn up for White but I am not able to say if it wins or not, but it's the best practical chance for White.